JP Journal of Algebra, Number Theory and Applications
Volume 3, Issue 2, Pages 327 - 336
(August 2003)
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LINEAR MAPS PRESERVING {1,
2}-INVERSES OF MATRICES ON SYMMETRIC MATRIX ALGEBRAS OVER FIELDS OF CHARACTERISTIC NOT 2
Xian Zhang (U. K.)
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Abstract: Suppose
F is a field of characteristic not 2.
Let and
be
the
full matrix algebra and symmetric matrix
algebra over F, respectively. All
linear maps from
to
(respectively,
preserving {1, 2}-inverses of matrices are
characterized. As a medium step, a similar
canonical form of a matrix triple is
also obtained. The similar canonical form
simplifies the process of characterizing
linear maps from
to
preserving -inverses
of matrices. |
Keywords and phrases: field, characteristic, {1, 2}-inverse of
matrix, linear map, full matrix algebra, symmetric
matrix algebra, similar canonical form. |
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